DESCENDING CHAIN CONDITION RELATIVE TO A TORSION THEORY

被引：43

作者：

MILLER, RW ^{[1
]}

TEPLY, ML ^{[1
]}

机构：

[1] UNIV FLORIDA,GAINESVILLE,FL 32611

来源：

PACIFIC JOURNAL OF MATHEMATICS | 1979年 / 83卷 / 01期

关键词：

D O I：

10.2140/pjm.1979.83.207

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A well-known theorem of Hopkins and Levitzki states that any left artinian ring with identity element is left noetherian. The main theorem of this paper generalizes this to the situation of a hereditary torsion theory with associated idempotent kernel functor σ. It is shown that if a ring R with identity element has the descending chain condition on σ-closed left ideals, then R has the ascending chain condition on σ-closed left ideals. © 1979, University of California, Berkeley. All Rights Reserved.

引用

页码：207 / 219

页数：13

共 14 条

[1] DIRECT-SUM REPRESENTATIONS OF INJECTIVE MODULES [J].